At home later that day I looked up modes on Wikipedia. Then I got out my Led Zeppelin Complete (to 1973, anyway) songbook and tried to play through Dancing Days. It was a bit tough with all the ledger lines as it's a piano-vocal rather than bass score. I started flipping through the rest of the book as I love so many songs on both Houses of the Holy and IV (or ZOSO, whatever), and landed on Four Sticks. It took awhile to figure out which mode this song was in, as the key signature was A, but every G had a natural sign, and the song clearly wasn't in either A major or the relative minor, F#. Eventually I figured out that the verses were in E Dorian, and the choruses in A mixolydian.
I was excited to share my discovery with Steve today. At first he said no, it's A mixolydian, but then he realized that I was right, as the tonic-sounding note for the verses is E, not A. He explained that the two modes in this song were actually contiguous, with the verses starting the scale on E and the choruses on A, which made sense. He praised my intellect, and suggested I transcribe the song with the key signature of D major, which would make more sense, as then all the G natural accidentals could be avoided.
I'm still working on Low Spark and Black Orpheus as well, both of which are a hell of a lot easier to sing than Robert Plant's screaming alto parts, but I do love Led Zep. And I'm excited to learn about modes, and re-learn minor scales, and generally feel like I'm becoming a more competent musician every day.